Top Republicans are privately pressuring Florida Sen. Marco Rubio to run for re-election over fears that the party could lose his seat in the November election.

"We hope he would reconsider running for reelection, which would really increase our chances to hold the seat," Scott Reed, a key strategist at the U.S. Chamber of Commerce, told CNN. "He is a proven vote-getter and this Senate seat could be pivotal to the majority."

Rubio, has said that he would leave the Senate after his term ends in January, is resisting, according to the report. He quit the race for the Republican presidential nomination in March.

The filing deadline is June 24.

"It's the Republican nightmare nobody wants to talk about," Josh Holmes, a former chief of staff to Senate Majority Leader Mitch McConnell, told CNN. "Everyone knew it would be next to impossible to replace Marco Rubio, but I don't think anyone appreciated how steep that drop-off actually is in Florida."

Among the names being bandied about, according to the report, are Reps. David Jolly and Ron DeSantis; business executive Carlos Beruff; entrepreneur Todd Wilcox and Florida Lt. Gov. Carlos Lopez-Cantera.

Alex Burgos, a Rubio spokesman, told CNN that the senator was not reconsidering his decision — referencing his earlier statements that he would become a "private citizen" after leaving office.